. Let ƒ be a function and all we know about it is (a) The derivative of f is equal to the derivative of x³ for all real numbers, and (b) ƒ (2) = 10. Find a formula for f (x).

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: a) For x>, the derivative f'(x) equals the number b) For <, the derivative f' (x) equals the number…

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Q: Which statement is true? O There can only be one anti-derivative, f(x), for a function g(x). There…

A: Given query is to find the correct statement.

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = (1 −…

A: The equation of the function  f(x) = (1 − x)(x2 − 3)2

Q: The graph of the continuous function g, the derivative of the function f, is shown above. The…

A:

Q: Find the equation of the tangent line to the graph of the given function at the given value of x.…

A:

Q: a. Find the derivative of f at x. That is, find f '(x). b. Find the slope of the tangent line to the…

A: Given,           fx=-4x+1 ; x=-1 , x=2

Q: if f(x) is a function with derivative f'(x)= (x^2 + 1)^5, then the following is true about f(x)

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Q: A) p'(-2) 0 p'(0) < 0 E p'(0) = 0

A: given: the graphs of the functions f(x) and g(x) are given. the functions f and g are…

Q: let f(x)=(x-9)(4x+5). Find an equation for the tangent line to the graph of f at x=12.

A: Given, The function is f(x)=(x-9)(4x+5)

Q: 23. Find the derivative of the function. f(x) = 6sin?(-5x8) %3D f'(x) = %3D

A: Here is the solution of the given problem. Derivative: By chain rule

Q: Find the first and second derivative of the function. Check to see that your answers are reasonable…

A: find out the first and second derivative.

Q: The graphs of the differentiable functions f and g are shown above. If the function p is defined by…

A: Given:- p(x) = f(x) g(x)  To find:- Sign of p'(-2) and p'(0) from given graphs

Q: 1) Find the hundredth derivative of p (x) = (x + x° + x')'º(1 + x²)'' (x³ + x° + x'). Justify your…

A: Here we have to find the hundredth derivative of p(x)=(x+x5+x7)10(1+x2)11(x3+x5+x7) .

Q: Find the function f given that the slope of the tangent line to the graph of f at any point (x,…

A:

Q: If f is the function whose graph is shown, let h(x) = f(f(x)) and g(x) = f(x²). Use the graph of f…

A: Given: The graph of f(x) is given as:

Q: Suppose L is a function such that L'(x) = 1/x for x > 0. Find an expression for the derivative of…

A: Given:- Suppose I is a function such that L'(x) = 1/x for x &gt; 0. To find:- An expression for the…

Q: The derivative of a sum of functions is the sum of the derivatives of each function. O True O False

A:

Q: Find the derivative of the following functions at a given point x = a (3) (g) f(x) a = 4.

A:

Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

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Q: Find an equation of the tangent line to the graph of the following function f at the specified…

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Q: Which of the following must be true? The derivative of the anti-derivative of f (x)is f (x) The…

A: Solution of given question is followed by:

Q: Suppose that a function f(x) has derivative f' (x) = g(x)+ h(x) for some functions g(x) and h(x).…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: If f and g are the functions whose graphs are shown, let u(x) - f(g(x)), v(x) - 9(f(x)), and tw(x) =…

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Q: If f and g are the functions whose graphs are shown, let  u(x) = f(g(x)),   v(x) = g(f(x)), and…

A: The given graphs of f and g are

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

A:

Q: (0. §) Find the equation of the function f whose graph passes through the point and whose derivative…

A: you can clearly understand if you follow the below solution

Q: Which of the following statements is NOT true about the derivative of the function? The derivative…

A: The geometrical meaning of derivative is , the slope of the line segment tangent to the function…

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

A: see below the calculation and answer

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

A: x      f(x)    g(x)     f1(x)    g1(x)      3      1      4      6     3      4…

Q: On what interval is the function f(x) .2 increasing, if the derivative of f is f(x) = (x – 2)* (x +…

A:

Q: The graph of the second derivative of a function f(x) is shown at right. Which of the following…

A: Given graph is

Q: Consider the following f(x)=1/2x In x^2, (-1,0) Find an equation of the tangent line to the graph…

A: Tangent  line to be find

Q: Let g be a function that is defined for all x, x + 2, such that g(3) = 4 and the derivative of g is…

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Q: Which of the following statements is TRUE? a. If f '(3) = 5 and g '(3) = 4, then the graph of f (x)…

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Q: Let f(x) = x³ – 4x. Calculate the difference quotient f(3+h)-f (3) for - h = .1 h = .01 h = –.01 h =…

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Q: The derivative of the function f(x)= 1- In xr is: -1 -x f'(x) = f'(x)= 2x/1- In x 2/1- In x O This…

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Q: A function, f (x), has derivatives: f'(x) = x² (x – 3) f"(x) = 3x(x – 2) Which of the following…

A: Consider the derivatives of the function fx f'x=x2x-3f''x=3xx-2 First, find the original function…

Q: 1) 2 a) Let f(x)=√x +4. Use the definition of the derivative to find f'(x). Find f'(5) by two…

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Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

Q: of the tangent line to the graph at any point (x,f(x)) is f'(x) and that the graph of f passes…

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Q: 5. Let f(x) = 5x4 - -2+8√√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: C Suppose that the second derivative of a function f(x) is given by f"(x) = (x – 4)(x – 7)² In() %3D…

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Q: Let f(x) 2x. Calculate the difference quotient f(3+h)–f(3) for h h = .1 h = .01 h = -.01 h = -.1 If…

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Q: 1. Consider the function f(x) given by its graph at which the points C, E and H are the inflection…

A: Let's find.

Q: If f is the functions whose graph is shown, let h(x) = f(f(x)) and g(x) = f(x2). Use the graph of f…

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Q: 7 f'(x) = X. 2 (3,7 /3 -

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Q: 5 Let f(x) =x -e*. Find the value of x for which the second derivative f“equals zero. 2

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Q: 1. The figure below shows the graph of f', the derivative of the function f, on the closed interval…

A: Given

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: