Question

Two hard calculus problems help?

Answer 1

Find the critical number of the function.
g(t) = | 6t - 9 |
t =


Find the critical points of the function.
F(x) = x^4/5(x - 7)^2
x = (smallest value)
x =
x = (largest value)

Answer 2

Relative minimum of the graph of |6t - 9| is at (1.5, 0) and the derivative of g(t) at 1.5 is undefined (one-sided limits are different)
Thus, critical number is t = 1.5

To find the critical numbers, find when f'(x) = 0 or is undefined
f(x) = x^4/5(x - 7)^2
f'(x) = [4x^3(5(x - 7)^2 - 10(x-7)*x^4]/(25(x-7)^4)
f"(x) = [20x^3(x - 7)^2 -10x^4(x - 7)]/(25(x-7)^4) which reduces by (x - 7)
f'(x) = [20x^3(x - 7) -10x^4]/(25(x - 7)^3)
setting the numerator = 0 and factoring
10x^3[2(x - 7) - x] = 0
10x^3 (x - 14) = 0
x = 0 , x = 14 are two critical numbers

The denominator = 0 at x = 7 (undefined)

0, 7, 14

Answer 3

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