28 For the function f(x) = state if a power function. If so, write it in the form f(x) = kx' and state the values of k and p. If not, type N for the values of both k and p. Is it a power function? O A. Yes O B. No The function in the form of f(x) = kxP, k =and p =.

Q: 1. From our class discussions, recall that (2") = na"-, : (z"). and 유(a")-(a") In a Apply the Power…

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Q: 4.20 Consider the function f(x) = x' – 2x + 4 on the interval [-2, 2] with h = 0.25. Use the…

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Q: The function f(x) = 2a – 392? + 240x – 4 has two critical numbers. The smaller one is x = and the…

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Q: 22. The function f(x) = Vx – 6 is transformed according to (x, y) → (7x – 7, - y+1). the transformed…

A: Substitute fx for y in the transformation and simplify. x,y=x,f(x)→7x-7,-f(x)+1=7x-7,-x-6+1

Q: find all possible functions with the givenderivative. y' = √θ

A: We first separate the variables

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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A: Given: f(x) = x − 6/x satisfy the conclusion of Mean value theorem in the interval [1, 3].

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Q: Consider the following function. g(x) = -x2 + 9x + 6 Find the first and second derivatives of the…

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Q: For the function f(x) = 3x²-x³-4 where -3 ≤ x ≤ 3, complete the following. 1. Find f' and f". 2.…

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Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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Q: When we introduced the quotient rule, we didn't actually prove it. Let's do that using only the…

A: Given Data: Function: fxgx=fx·gx-1   The chain rule for derivative is, ddtfgt=f'gtg't ......1   The…

Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

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Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

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Q: Find the first derivative f' and the original function f. f"(x) = x³ – 18x, f' (1) = 0, ƒ(1) = 8…

A: Given query is to find f(x) from f"(x).

Q: Suppose a tour guide has a bus that holds a maximum of 110 people. Assume his profit (in dollars)…

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Q: Given the function g(x) = 8x – 84x? + 240x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: The function f is defined by f(x) = \25 – x² for -5 sx 5. (a) Find f'(x). (b) Write an equation for…

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Q: 3) Let f (x) = e=x² Where is y'> 0? What does this tell you about the original function?

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Q: A long distance company charges a monthly fee of $4.95 and $0.02 per minute. Let f(x) be the monthly…

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Q: For −10≤x≤14the function f is defined by f(x)=x^3(x+3)^4 On which two intervals is the function…

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Q: 4. Find the range of the function F(x)=√36-t² dt O [0, 36π] O [0, 18π] O [-6, 6] O [-6, 0]

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Q: 1. Given the function f(x) = Vx5 – 3Vx², find the interval(s) of increase.

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Q: 4. Determine the value of the constant k so that f(x) = e* (x + k) decreases on the intervals (- 0,…

A: we have to find value of k

Q: x-2 For the function 10x) = ind f(X), the third denvative of t and i ), the fourth derivative ofT…

A: Please refer the attached image for complete solution.

Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

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Q: 7) Find the difference auotient. f(x+h)-f(x) for the function, f(x) = x² + 3x - 4.

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Q: Q4: Find and classify all critical points for the function: z2 = (x3/3)-(y3/3)+2xy

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Q: (A) Find the absolute maxima and minima for ,3 Y = x + 5 over [-V2, v2). (B) Use the second…

A: y = x33-x+5y' = 3x23-1y' = x2 -1x2-1 = 0x2 = 1x = ±1

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Q: For – 12 < x < 14 the function f is defined by f(x) = r'(x + 5)° On which two intervals is the…

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Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: On the graph of f(x)=secx and the interval [−2π,0), for what value of x does f(x)=1? Choose all…

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Q: 4. a) Find the value of x where the function f(x) = (x – 4)5 is not differentiable.

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Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

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Q: (1) For every natural number n, x" = nx"-1 (you may use the product rule for derivatives and that x…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: 17 The function f is defined by f(x) = 5x - c, where c is a constant. In the xy-plane, the graph of…

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Q: nd all critical numbers for the function x1/3 f(x) = + 8. x² + 3

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Q: if i have the function how would i use FTC(1) and the chain rule to find g'(x)

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Q: (2) For the function f(x)=--x² – 24x +19 3 (i) Determine the turning points and the values of the…

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Q: find all possible functions with the givenderivative. y' = -1/x2

A: Given: y'=1x2

Q: 9x Find the derivative of the function f(x)=In x2+15 2x O f'(x)= x²+15 15-x2 f"(x)= x2+15 2x O…

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Q: (A) Find the absolute maxima and minima for x3 y = - x + 5 over 3 [-V2, v2]. (B) Use the second…

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Q: The function f (x) = (8x + 1)e2“ has one critical number. Find it. X =

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Q: The population (in millions) of a country as a function of time t (years) is P(t) = 30 · 20.1t .…

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Q: 4. a) Find the value of x where the function f(x) = (x – 4)3 is not differentiable.

A: According to power rule of differentiation , .

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: The given functions are: fx=2x2-1x2+3x2+1 and gx=x2+872-3x25 The person's brother believes that,…

Q: #8

A: Given:The decrease in weight from 487 pounds to 130 pounds in 8 months.