Let f be the linear function f(x) = -3x + 7. (a) The rate of change of f is (b) The graph of f is a ---Select--- + with slope and y-intercept

Q: Use the limit definition to calculate the derivative of the linear function. f (x) = 7x − 9

A: Plug the given function in the limit definition of the derivative

Q: Use the second-derivative test, if possible, to find relative extrema of y x5 – 5x. -

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Q: Find the derivative of  g(z) = 4z7-3z-7+9x

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Q: Find the derivative of y = 2 + v2 + vx5 |2 + V2 + Vx5

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Q: Find the derivative of the function. x2 + 3 y = x² – 3

A: Consider the given function y=x2+3x2-34

Q: Determine the derivative of a quadratic function of general form y=ax2+bx+c.

A:

Q: Use the Chain Rule to find the derivative of the function. y = (2x2 − 3)3 y' =

A: The chain rule to find the derivation is,

Q: Find the average rate of change of g(x) = 4x + 2 between the points (-3,-10) and (3,14)

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Q: Use the Chain Rule to find the derivative of the function. y = (x3 + 5x2)−1 y' =

A: The function is given by,

Q: Use the Chain Rule to find the derivative. y = (x4 - x3 - 1)2/3

A: To find the derivative y = x4 - x3 - 123.

Q: What is the rate of change of the function y = - 2x – 1?

A: The rate of change

Q: =) f(x) = x²e¬4x

A:

Q: Use the Chain Rule to find the derivative of the function. y = (3x2 - 7)3

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Q: The derivative of f(x,y)=x^3+y^2 is 3x^2+3y^2. True or False?

A: The given function f(x, y) = x3+y2 Differentiate with respect to x ∂f∂x=3x2 Differentiate with…

Q: ƒ(x) = (x³ – 4x) 10

A: Solve the derivative

Q: Use the Chain Rule to find the derivative. f(x) = (x5 – x3 – 1)2/5 %3D

A:

Q: Use the chain rule to find the derivative of f(r) 3e7z° +6z7

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the slope of the curve y=x4 at x=3.

A: Find the slope of the curve y=x4  at    x=3.

Q: Apply the second derivative test to find all relative extrema. (b) f(x) = -x + 4x³ +8x²

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Q: Find the average rate of change of g(x) = 3x² – 2 between the points (-4,46) and (3,25) -

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Q: Estimate the derivative of the function f (x) = - – 3 at the point x = 3. 3 3 1/5 1/3

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Q: what is the gradient of f(x)=3x2-2x at x=-2?

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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: How fast does the  slope of the curve y= (x2+x+1)2 change at the point where x=2

A: First derivative of a function represents the change in function or slope of the function and second…

Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

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Q: f(x) = (x + 2)(2x² – 3) %3D

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Q: Use the Chain Rule to find the derivative of the function. y (4x2 - 7)3 %3D

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Q: Find the average rate of change of f(x) = 3x2 - x from x1 = -1 to x2 = 2.

A: The given function is fx=3x2-x.

Q: the derivative () of = f(x) = 2

A: Please refer to the image below

Q: Use the chain rule to find the derivative of f(x) = 2e-72° + 32® f' (x) =

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Q: The curve has a gradient function 2x - 3 and passes through (1,-6). Find the value of x when y = 0

A: Clear solution is given.

Q: Find the derivative of y = xArcsinx + V1 – x².

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Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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Q: 4 - 1 У — уз - 1

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Q: Find the derivative. Using Chain Rule y = (2x2 – 1)3(3x² + 1)³ |

A: According to question,Given Function,y = 2x2-133x2 + 13

Q: Use the chain rule to find the derivative of f(x) = 2e5a* + 9x³ %3D f' (x) =

A: We have to find

Q: Test f(x) = (x3/3) +2x2-5x+1 for relative extrema, using the second-derivative test where possible.

A: For a given function,f(x), at relative extrema x=a, f'(a)=0.The second derivative test is applied to…

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: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1

Q: Find the derivative of the function. f(x) = V3 - 6x2 %3D f'(x) = || %3D

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Q: Find the gradient of the curve . Y=4x^2 at x=3

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Q: the point (-2, 0). Find the minimum rate of change of f(x, y) = x²e-2y at

A: Given: A function f(x, y)=x2e-2y and a point (-2, 0). To find: The minimum rate of change of a given…

Q: Find the derivative of the function. -5x3 + 3x + 2 y = dy -10x +3 - 2x2 dx dy -5x +3 + 2x2 dx -10 -…

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Q: Use the chain rule to find the derivative of f(x) = 4( – 5æ" + 3z")" %3D

A:

Q: The function f (x) = ax³ – bx² has a gradient of 2 at point (1,6). Find its gradient when x = 2.

A: Given  f(x) = ax3-bx2

Q: find the average rate of change of f(x) = -x3+3x2 from x=-1 to x=4

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Q: Differentiate the function y=(1−x)3 without using the chain rule.

A: Differentiation: y=(1-x)3 y=1-3x+3x2+x3ddx(xn)=nxn-1

Q: Find the average rate of change of g(x) = 5x2 + (5)/(x4) on the interval [-4,3].

A: Given, g(x)=5x2+5x4 And given interval is -4, 3

Q: Determine the derivative. x – 2x + а) у- x+3 b) y = n(4x² – 5x)

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.