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Finding the Derivatives in Calculus

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Q#8. For f(x)=2-5X^2, Find:

i) f`(x).

Answers:
a. -5x
b. -10x
c. -10x
d. 0

Q#9. Consider f(x)=3-4*Square root(X)

i) Find f`(x)

Answers:
a. - square root of X / 2
b. - 4 / square root of X
c. -2/square root of x
d. -8 / Square root of x.

Q#10. Consider f(x)=3x/x+9

i) find f`(x)

Q#7. A personal computer salesperson receives a base salary of $3000 per month and a commission of 4% of all sales over $30,000 during the month. If the monthly sales are $60,000 or more, the salesperson is given an additional $600 bonus. Let F(s) represent the person`s earnings during the month as a function of the monthly sales.

a) Find lim F(s)
s---30,000

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Solution Summary

This problem set consists of four questions. Three of them involve finding the first derivative, and one involves finding a limit. The solution explains how to find the solutions using the power rule, the quotient rule, and an explanation of limits.

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Q#8. For f(x)=2-5X^2, Find:
i) f`(x).

Answers:
a. -5x
b. -10x
c. -10x
d. 0

Use the power rule to find the derivative.

power rule: the derivative of xk is kxk-1 if k is a constant.

Here, the derivative of x2 is 2x1. Also remember that the derivative of a constant is 0.

f(x) = 2 - 5x2

f'(x) = 0 - 5(2x1)
f'(x) = -10x

The answer is b and c (they're the same!).

Q#9. Consider f(x)=3-4 Square root X.
i) Find f`(x)

Answers:
a. - square root of X / 2
b. - 4 / square root of X
c. -2/square root of x
d. -8 / Square root of x.

Use the power rule again, remembering that the square root of x is the same as x^(1/2).

f(x) = 3 - 4x1/2

f'(x) = 0 - 4(1/2)(x1/2 - 1)
f'(x) = -4(1/2)(x-1/2)
f'(x) = -2x-1/2

This ...

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