Assuming f and g are differentiable functions, determine ) (2) if f(2) = 5, f' (2) = -7, 9(2) = 8, and g'(2) = 4.

Q: 9. State the Second Derivative Test for functions of two variables z = f(x, y)

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Q: Find the critical points of the function. Then use the Second Derivative Test to determine whether…

A: Critical points make a difference in the behavior of the function. That is, at each critical point…

Q: Find the equation of the tangent line to the function f(x)=−3x2−2x at the point where x=1. Give your…

A: Here we find the equation of tangent line of the function fx=-3x2-2xat x =1

Q: Does the function cos x х f(x) = 0, x = 0 have a derivative at x = 0? Explain.

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Q: Find the derivative of f(z) = e2" (3z2- z)

A: Given, f(x)=e2x(3x2-x) Here, when we try to find the derivative of f(x), both chain rule and…

Q: State the limit of the derivative f’(x) = square root of x+3, f’(2)

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Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

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Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: Using the limit definitoin of the derivative, comput the derivative of the function. x^3+3x^2+x+3…

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Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

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Q: Find the derivative of the function = V(=² – 3)* 6, f(x) at x = 2. %3D f'(2) =

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Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

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Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x>0…

Q: a, b, and I are differentiable functions of the same variable what is the derivative of H ac b +…

A: To find the derivative of acb, here a,b and c are differentiable function of same variable. Let a,b…

Q: Find the derivative using the definition of the derivative for f(x) = Vx (ie. f'(x) = fn &+h)-{(x) ,…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

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Q: . Does the function cos x x + 0 f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A: Consider the given function fx=1-cosxx        x is not equal to 0x=0

Q: 6. Using the limit defenition of the derivative, find the equation of the line tangent to the curve…

A: We have to find the slope of the tangent line at first.Then we find its equation.

Q: ion ƒ(x) is infinitely differentiable and that f'(x) = - st, second, third and n-th derivative of f…

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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: Find and classify the relative extrema of the function, if they exist. You MUST use the…

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Q: The maximum rate of change of the function 1 f(x, y) = at the point (1, -2) happens in direction of…

A: I have find the direction and value of maximum rate of change of given function and say that given…

Q: Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the…

A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

Q: 2. Using the definition of derivative, prove the following: (a) fo= if s)-V (b) y-sec'x if y tanx

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Q: Solve for the derivative of t y =2 V3-z Previous

A: This is a basic differentiation problem

Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x= 5, assuming…

A: GIVEN      Y= fx+1fx+x

Q: Suppose that f(x, y) = x*y². The directional derivative of f(x, y) in the directional and at the…

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Q: Suppose that f(x, y) = x°y. The directional derivative of f(x, y) in the directional (– 2, – 1) and…

A: Explained below

Q: The slope of the tangent line to the differentiable function f at the point (2, f(2)) is…

A: It is given that the slope of the tangent line to the differentiable function f at the point 2,f2 is…

Q: Using central difference, find the second-order derivative of y=x²cosx at x=9, h=0.1

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Q: Using the definition, find the derivative of fz) = 3 z^-6 z² at point z= 0

A: Given,          fz=3z4-6z2

Q: find the equation of tangent line of function f(x)=csc(x)-cos(x)1/2 at the point ((2*3.14)/3,…

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Q: True or false The slope of th tangent line to a dfferentiable function f at the point (2,f(x)) is

A: The slope of the tangent line to a differentiable function f at the point (2, f(x)) is

Q: Find the derivative of the algebraic functions f(x) = x (1-) x+3, : g(x) = x + cotx

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Q: HW prove That The derivative of Flx)=x-x is if (x) = 3x?1 use definition of devivativeto finid The…

A: Use following mentioned rules to find the derivative of the function. The power rule of…

Q: are differentiable at a, then prove the sum and product rules for derivatives. If f, 9

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Q: Find and classify the relative extrema of the function, if they exist. You MUST use the…

A: Given :fx=2xx2+1

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: 13. Suppose a continuous function f and its derivative f' have values table. Given that f(1) 2, use…

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Q: The first derivative of a continuous function y = f(x) is y' = x(x- 21). Find y" and then use the…

A: Given: i. The first derivative of a continuous function y=fx.ii. y'=xx-212 To Find: i. y''ii. Use…

Q: Find the points on the graph of f where the tangent line is horizontal.  f(x)=(x^2+8)(5-x) larger…

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Q: Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate…

A: Average rate of change of constant function fx=b Rewrite;              y=b…

Q: The derivative of the function y=f(x) at the point x=c is characterized as the of the function at…

A: We have to tell what is derivative of function y=f(x) at x=c called ...  a. Slope  b. Point of…

Q: Using differentiation rule, find the derivative of the function ƒ (²) = [2 + (² ² + 1)²³ at _z = 1 +…

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Q: Find all possible functions with the given derivative. 1. If y 1, then y %3D 2. If y = a, then y 3.…

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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 derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Given :   f(x)=x4 , at x=3/2 f(x)=1/4 , at x=2