Question

1. Let f(x)=−x^2+13x+4

a.Find the derivative f '(x)

b. Find f '(−3)

2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded to 2 decimal places.

f '(3)=

3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).

f '(x)=

4. Find the derivative of the function f(x)=√x−5/x^4

f '(x)=

5. Find the derivative of the function f(x)=2x−5/3x−3

f '(x)=

6. Find the derivative of the function g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your answer.

g '(x)=

7. Let f(x)=(−x^2+x+3)^5

a. Find the derivative. f '(x)=

b. Find f '(3)=

8.

Let f(x)=(x^2−x+4)^3

a. Find the derivative. f '(x)=

b. Find f' ′(-2)=

9. Let f(x)=2x^2−4x+3/3x^2+2x+11

Evaluate f '(x)=4 rounded to 2 decimal places.

f ′(4)=

10. Let f(x)=(3x−5x^3)/(3+√x)

find f '(x)

f '(x)=

11. Find the derivative of the function f(x)=√7x+4

f '(x)=

Answer #1

find the derivative of the function
f(x)=(4x-3)^5(2x^2+5x-8)^2

Verify the quotient rule for each of the following:
1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2
2. f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1

i) Simplify the following equations 3(2x – 5) – 2(5x - 7) + 9 =
ii) Solve 3x – 2 divided by 2= 4x - 5 divided by 4 (5marks)
c) Solve the following pairs of simultaneous equations 2x + y =
7 and x - 2y = -1

solve for x using the factor theorem and long division. a.
2x^3-3x^2-5x+6=0 b. 8x^3+4x^2-18x-9=0 c.
2x^3+10x^2+13x+5=0 d. -2x^3-12x^2+x+60=0

Find the derivative of the function.
(a) f(x) = e^(3x)
(b) f(x) = e^(x) + x^(2)
(c) f(x) = x^(3) e^(x)
(d) f(x) = 4e^(3x + 2)
(e) f(x) = 5x^(4)e^(7x+4)
(f) f(x) = (3e^(2x))^1/4

1020) y=8/sqrt(4x^7)=Ax^B + C. y'=Kx^F + G. y'(9)=H. Find A,B,C,K,F,G,H. ans:7
1026) Find the derivative of y=(5x^(1/4) - 8x^(1/7))^3, when x=2. ans:1
1010) y=3x^2 + 2x + 5 and y'=Ax^2 + Bx + C. Find A,B,C. Next Question:
y=(x^2)/7 + x/4 + 2 and y'=Hx^2 + Fx + G. Find H,F,G. ans:6

1. Given f(x)=2x^3-3x^2+4x+2, find (f^(-1))'(14).
Differentiate and Simplify
2. f(x)=ln(3x) e^(-x^2 ) (Answer with positive exponents
Integrate and Simplify 3. ∫▒(6x^2-5x)/√x dx

Let f(x) = 4x^5 − 5x^4 + 9.
(a) Find each critical number for f.
(b) Apply the First Derivative Test to each critical number
found in part (a), being careful to explain what conclusions (if
any) you can draw.
(c) Apply the Second Derivative Test to each critical number
found in part (a), being careful to explain what conclusions (if
any) you can draw.

1)If f(x)=2x-2 and g(x)=3x+9, find the following. a)
f(g(x))=? b) g(f(x))=? c) f(f(x))=?
2)Let f(x)=x^2 and g(x)=6x-16. Find the following: a)
f(3)+g(3)=? b) f(3)*g(3)=? c) f(g(3))=? d) g(f(3))=?
3) For g(x)=x^2+3x+4, find and simplify
g(3+h)-g(3)=?
Please break down in detail. Please and Thank
you

Consider the function f(x) = x^3 − 2x^2 − 4x + 7 on the interval
[−1, 3]. a) Evaluate the function at the critical values. (smaller
x-value) b) Find the absolute maxima for f(x) on the interval [−1,
3].

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