8. (Optimisation.) The function f(x) = 2x³ - 3x² - 12x+80 has domain 0 ≤ x ≤ 4. Your goal is to find the value of a that minimises this function over the given domain. Follow the steps below. • Identify the endpoints of the domain. • Find f'(x). • Solve f'(x) = 0. • Collect all critical points for this problem. • Identify the minimum.

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A: Given function is fx=-3x+4, x&lt;-2x2-2    ,x≥-2.

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A:

Q: solve f´(2) if f(x) = x^3 – 6x^2 + 9x + 3 a).  For which x is the function decreasing? Show using…

A: According to the given information,

Q: 7 -1,-2.5) 0-5) ,0- S (1-10) 14 -21 (2,20) y-intercept End Behavior: As x oc as x OC

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Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

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Q: Compute the number of units x that determine the maximum profi

A: Given that: Cost function , C(x)=30x+100Revenue function, R(x)=-x2+90x

Q: Describe the end behavior of each function. 7) f(x)= x -2x'+x-1 8) f(x)=-x² + 8x - 17

A:

Q: 1. Find f'(x), f"(x), and f(x) for the following functions. a. f(x) = (2-3x)5 b. f(x) = 2¹2 +324 c.…

A:

Q: Consider a pizzeria that sell pizzas for a revenue of R(x) = ax and total cost of C'(x) = b + cx +…

A: Given R(x)=ax ,C(x)=b+c x+d x2 a. profit P(x)=R(x)-C(x)                   =ax-b-cx-dx2 b. P'(x)=…

Q: 1. f(z +h) – f(x), h #0 : f(w) – f(x) r h - 2. ', x # w : -3<x3 w - x

A:

Q: If F'(x) = f(x) and F(0) = 0, find F(b) for b = 3, 5, 7, and 9.

A: Given graph of f(x)

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Q: 2. If f"(x) = 4sinx+16cosx, f(0) = 6, f'(0) = 1, find f(x) and f(4).

A:

Q: For what values of the parameter 'a' does the function f (x)=x³+3(a - 7)x² +3(a? -9)x - 1.have a…

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Q: 1. f(x) = x² − 16x, [3, 10] 2. f(x) = 15 – 2x − 2x², [1, 2] 3. f(x) = 2x³ + 3x² − 12x + 24, [−4, 0]

A:

Q: 7. 1. f(x) = 6 /x? - 20 x + 4 find f (4) (x). 收 .5 2. x-xy+y 3, find y".

A: 1) fx=6x23-20x45+7x57+4x6fx=6x23-20x45+7x-57+4x-16Differentiating with respect to…

Q: f(x) = x(6 – x)-

A: Given :f(x)=xa(6-x)b 0≤x≤6