Suppose that the function with the given graph is not f(x), but f'(x). Find the open intervals where the function is concave upward or concave downward, and find the location of any inflection points.

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: use the definition of derivative to find f prime (x). f(x)= 3(2x-1)^3

A: Given function is fx=32x-13. To find the derivative of the function using definition of derivative.…

Q: Determine the derivative of the cube root function f(x)=3√x using the limit definition.

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Q: For the function, f(x) = 9x² – x³ - a. Use the derivative to find all critical points b. Classify…

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Q: Find the slope of the tangent line to the graph of f(x) = x³ + x at x = 3 using the limits…

A: Given- fx=x3+x To find- The slope of the tangent line to the above function at x = 3 using the…

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x²-6x+5.

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Q: Calculate the derivative of f(x)=4x³ with respect to x and evaluate this derivative at x=2.

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Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: Use the first derivative test to determine the local extrema, if any, for the function f(x) = 3(x -…

A: Given that a function f(x) and we find local extrema. For local extrema we do first derivative of…

Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x³-8x+9.

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Q: Suppose the second derivative of f(x) is given by f''(x) = 15x6(x + 9)5(x2 + 36). Determine the…

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Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: find the function with the given derivative whosegraph passes through the point P. ƒ'(x) = 2x - 1,…

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Q: Find the second derivative for the functions defined as follows ƒ(x) = (x2 - 1)2

A: Given function: fx=x2-12 fx=x4-2x2+1 Differentiate the equation w.r.t "x"…

Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Suppose that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Given: The  slope of  a curve:   To determine: The equation of the curve f(x)

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

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Q: If f(x) = 24x + 2, use the limit definition of the derivative to find the instantaneous rate of…

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Q: For the function f(x) x + x3, find all of the relative and absolute extrema using the first or…

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Q: Find the derivative of the function f(x)=2x2 using the limit definition.

A: Limit definition of derivative of f(x) is  f'(x)=limh->0f(x+h)-f(x)h

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: Use the fact that the derivative of the function ​f(x)=4/x is f"(x)=-4/x2 to find the equation of…

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Q: Use the fact that the derivative of the function g(x)=√x is g"(x)=1/2√x to find the equation of the…

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Q: Suppose the derivative of the function y = ƒ(x) is y′ = (x - 1) 2(x - 2)(x - 4). At what points, if…

A: It is given that, the function f(x) has the derivative

Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

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Q: 1. Find the derivative of f(x) = 3x³ + 2x using the limit definition.

A: We have to find derivative using definition.

Q: Suppose the derivative of the function y​f(x) is (x-1)^2(x-5)(x-2). At what​ points, if​ any, does…

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Q: Use the limit DEFINITION OF A DERIVATIVE to find the derivative of the function. 16) f(x) = Vx + 5…

A: The derivative of a function y=f(x) is given by f'x=limh→0fx+h-fxh. The given function is fx=x+5.

Q: Suppose that f is a function defined as f(x) = – 5x + 3x + ¤ + 3. Find an equation for the tangent…

A: Given function is: fx=-5x3+3x2+x+3 We have to find the equation of the tangent line drawn to the…

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: find the function with the given derivative whosegraph passes through the point P. g'(x) = 1/x2 +…

A: g'(x)=1x2+2x,P(-1,1) Formula ∫xndx=xn+1n+1+C

Q: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: Compute the Indicated derivative. 7. f" (x) for f(x) = 5x2-14x + %3D

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Q: Find the derivative of the following with respect to x: 1. f(x)=4log3x-In x

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Q: 3. Use the limit definition of the derivative to find the derivative of the function. a) f(x) = 2x²…

A: Given query is to find the derivative using definitely.

Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: Suppose that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Using integration.

Q: 2. Use the second derivative to find the inflection points and the intervals on which f(x) is…

A: For inflection point, Put f"(x)=0. For concave upward, f"(x) > 0. For concave downward, f"(x)…

Q: Find the derivative of f(x)= 11x^2 at x=1

A: Given:    f(x) = 11 x2  at x = 1

Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: Use the limit definition of the derivative to find f'(x) given f(x) = x² – 3x + 5.

A: Given function :

Q: Find the derivative of f(x) = 5x2 + x using the limit definition of the derivative.

A: We have to find the derivative of function using limit definition of derivative where function is:…

Q: *** Use the first and second derivative to sketch the graph of f(x) = In(x² +1). In particular,…

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Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…