Hey guys. These are the first AP Problems I'm doing. Here is all my work.(adsbygoogle = window.adsbygoogle || []).push({});

Let f be the function given by f(x) = x[tex]^{3}[/tex]-7x+6.

a. Find the zeros of f.

b. Write an equation of the line tangent to the graph of f at x = -1

c. Find the number c that satisfies the Mean Value Theorem for f on the closed interval [1,3]

So what I did is:

a. 0 = x[tex]^{3}[/tex] - 7x + 6

-6 = x(x[tex]^{2}[/tex]-7)

Final Answer: x = +/-1, 6

b. f'(x) = 3x[tex]^{2}[/tex] - 7

m = f'(-1) = 3(-1)[tex]^{3}[/tex] - 7 = -4

f'(-1) = (-1)[tex]^{3}[/tex] - 7(-1) + 6 = 12

Final Answer: y - 12 = -4(x+1)

c. f(b) = f(3) = 3[tex]^{3}[/tex] - 7(3) + 6 = -6

f(a) = f(1) = 1[tex]^{3}[/tex] - 7(1) + 6 = 0

f'(c) = (f(b)-f(a)) / (b-a) = (-6 - 0) / (3-1) = -3

-3 = 3c[tex]^{2}[/tex] - 7

Final Answer: c = 2[tex]\sqrt{3}[/tex] / 3

Please tell me what is right and wrong? I am fairly confident on a and b, but shaky on c because I haven't studied that yet and don't know if it's right at all.

Thanks in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# AP Style Problem - Derivatives

**Physics Forums | Science Articles, Homework Help, Discussion**