1. The deriative of the function f(x) is given by f\"(x)=6x^2+3. Find a formula
ID: 2884057 • Letter: 1
Question
1. The deriative of the function f(x) is given by f"(x)=6x^2+3. Find a formula for the function f(x) given that f(1)=25.
2.. Answer the questions below based on the following information about the function f. You must justify your answers.
1. The function f is continuous and di erentiable for all values of x.
2. f(x) > 0 for x < 0; f(x) < 0 for 0 < x
3. f'(x) > 0 for -6 < x < -2 and 5 < x
4. f'(x) < 0 for x < -6 and -2 < x < 5
5. f''(x) > 0 for x < -4 and 3 < x < 7
6. f''(x) < 0 for -4 < x < 3 and 7 < x
On which intervals is the function increasing?
What are the x-coordinates of the local maximums (if any)?
On which intervals is the function concave down?
What at the x-coordinates of the inflection points (if any)?
19. Let f(x) = x^3 - 5x^2 + 12
Find the slope of the line through the points (1; f(1) and (4; f(4)).
Verity the conclusion of the Mean Value Theorem by nding a number 1 < c < 4 where
the slope of line tangent to f(x) at x= c is the same as the slope of the line through
(1; f(1) and (4; f(4)).
Explanation / Answer
f'(x)=6x^2+3
Integrating both side using power rule for integration,
f(x)=6x^3/3 +3x +k
f(x)=2x^3+3x+k
Plugging x=1 and f(x) =25
25=2+3+k
k=20
f(x)=2x^3+3x+20
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.