What are the values f(4) and f 0 (4)

Q: 3. Determine the slope of the tangent at x = -1 on the graph f(x) = (5x² + 1)3.

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Q: Find the equation of the tangent line to the graph of f(x) = -2(3x – 1)³ at . Show work or explain…

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Q: The graph of f(z) = 2z³ + 12z² – 126z + 17 has two horizontal tangents. One occurs at a negative…

A: for the horizontal line find the slope first and set to zero.

Q: An equation of the line tangent to the graph of f(x)= x(1-2x) at the point (1,-1) is

A:

Q: Determine the coordinates of the point(s) on the graph of f(x) = 5x ^3 - 2x ^2 where the tangent…

A: Our aim is to determine the coordinates of the points on the graph off(x)=5x3-2x2 where the tangent…

Q: 4. Find the slope of the tangent to the graph of f (x) = x³ + 3x² + x at its point of inflection.…

A: Slope of the tangent is obtained by dy/dx

Q: The derivative of a certain continuous and differentiable function is given by: y = 3-x - 12-x +9.…

A: For maxima-minima, derivative of the function must be zero. That is,…

Q: The slope of a tangent to the curve f(x) = x² + 2x – 5 at the point (3, 10) is : 12 8. -5 10

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Q: Find all points (c, f(c)) on the graph of f(x) = x3 −3x2 where the tangent line has slope 9.

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Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (1,…

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Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A: Topic - tangent lines to curve passing through Given point outside curve

Q: Use the definition of a derivative to determine all points for the function f(x) = ((x+|x|)^2)+1 is…

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Q: How can you use the slopes of tangents to determine whether a function is increasing, decreasing, at…

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Q: I dont know where to start this problem. It would be great to have some help

A: Given:

Q: the tangent line to the graph (x^2 + 4)y = 8 at the point (2, 1).

A: Use formula of  equation of tangent  line

Q: Find the equation of the tangent to the graph of f(x) = x-3 at the point (5, 4). Start by evaluating…

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Q: Consider the function g(x)=(3x2-5x)(2x-3)(2x³+5x-6)(4x5-3x²+2x-8). Find the equation of the line…

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Q: Find an equation of the tangent line to the graph at the given point .

A: Given function: fx=16xx2+16  ……1   To find: Tangent line equation at point -2, -85.

Q: Find an equation of the line that is tangent to the graph of the function f(x)= 2x and parallel to…

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Q: find an equation of the tangent line f(x)=x+(6/x)    points (x,y)= (-6,-7)

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Q: The derivative of the function f is defined by f'(x) = x² - 3 sin (x - 5). What is the x-coordinate…

A: How to find absolute minima of function f(x) in a given closed interval: find the critical points…

Q: The function f is defined by f(x)=x/(x+2). What points (x, y) on the graph of f have the property…

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Q: 8. Using the second derivative test, find the maximum and minimum points for the function f(x)-x*…

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Q: The tangent line to the curve y = x3 - 6x2 - 34x - 9 has slope 2 at two points on the curve. Find…

A: Given,  The tangent line to the curve y=x3-6x2-34x-9 has Slope=2 at two points on the curve.…

Q: Find the equation of the tangent line to the graph of the function f(x)=4x3+5−−−−−−√ at the point…

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Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: Compute the slope of the secant line containing the points (1, f (1)) and D) on the graph of f (x) =…

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Q: Find the slope of the curve y=x^3-3 at the point ​P(-2,-11​) by finding the limiting value of the…

A: Given,y=x3-3Point P -2,-11The slope of the secant line ism=fb-fab-a

Q: Find equations of the two tangent lines to the graph of f(x) = x- that pass through the point (-1,…

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Q: rmine the coordinates of the point(s) on the graph of f(x) = 5x ^3 - 2x ^2 where the tangent line is…

A: We have to find the coordinates of the f(x)=5x3-2x2 where the tangent line is perpendicular to the…

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) =…

A: Given: fx=x+2x-22=y To find the slope of tangent line at point (6,4) ,we need to find the value of…

Q: 5. Determine the slope of the tangent at point (1,5) on the graph of f(x) = (9 – x²)} + 1.

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Q: Find the equation of the tangent line to the graph of the function f(x)= 2+5 z-8 at the point

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Q: 8. Using the second derivative test, find the maximum and minimum points for the function f(x)=x*…

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Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

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Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

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Q: ind an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: Given

Q: b) Use second derivative test to find absolute maximum and minimum values of f (x, у) 3 Зху — 6х —…

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Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

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Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: The line whose slope is 3 is tangent to the curve y=x² + 3x + 2 at the point, O (3,-2) O (-3,2) O…

A: The line whose slope is -3 is tangent to the curve y=x2 +3x+2 at the point. Here slope and line…

Q: Find the x value for all relative extremes of f(x) using the first derivative test. And specify…

A: Given,            f(x) =x2 - 15x - 15x + 1

Q: What is the slope of the curve y= 2 over √x at the point (4,1)

A: To find the slope at a particular point x=a, the first derivative of the function is taken. Once the…

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Given            fx=x-33x+4

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: Use the second derivative test to find the extreme values of the function f(z) = z-3z2-24z

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Q: Find the equation of the line that is perpendicular to the tangent line to f(x) = x4+1 at x = 2 and…

A: Answer and explanation is given below

Q: Estimate the slope of the tangent to the function f(x) = (x + 1)^2(x - 4) at the point of abscissa…

A: Introduction: A tangent line is one that intersects a curve at the so-called point of tangency.…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: