Question

Let f be the function given by f(x)=3x^4 +x^3 -21x^2

Answer 1

a.) Write an equation of the line tangent to the graph of f at the point (2,-28)
b.) Find the absolute minimum value of f. Show the analysis that leads to your conclusion
c.) Find the x-coordinate of each point of inflection on the graph of f. Show the analysis that leads to your conclusions

Answer 2

@phi

Answer 3

this looks like calculus
for a) find the derivative of your curve, and sub in x=2 to find the slope at that point.

once you have the slope, use the point slope formula for the equation of the tangent line.

Answer 4

kay i got y=24x-76

Answer 5

How about for part b.) and c.)

Answer 6

@phi

Answer 7

ok on a)

for the min, set the derivative = 0 and solve for x

see
http://www.khanacademy.org/math/calculus/derivative_applications/critical_points_graphing/v/minima--maxima-and-critical-points

it is short and helpful

Answer 8

@phi so my answer for a.) y=24x-76 is wrong?

Answer 9

or did u mean b.) not a.)

Answer 10

I said you were ok on a). That means your answer for a is correct.
the video is to help you finish the problem.

Answer 11

would it be easier if i divided the derivative by 3: 12x^3 +3x^2 - 42x=0?

Answer 12

of course, also factor out an x (x=0 is one solution)

Answer 13

so ishould factor out an x and 3 o:
3x(4x^2 +x - 14)?

Answer 14

3x(4x^2 +x - 14)=0

Answer 15

ok so i got 3x=0 (4x-7)(1x+2)=0
x=0, 7/4, 2

Answer 16

@phi

Answer 17

you mean x=-2

Answer 18

time to watch the video, and maybe the one after it where he does this same type of problem

Answer 19

oh yeah sorry i mean -2 :)

Answer 20

sorry i can't really watch the vid cause my cp is lagging x-x

Answer 21

so would x=-2 be the absolute minimum value of f?

Answer 22

@phi

Answer 23

see
http://www.wolframalpha.com/input/?i=f%28x%29%3D3x%5E4+%2Bx%5E3+-21x%5E2

Answer 24

ok how about for part c.)

Answer 25

@agent0smith can you help me with part c.) please? :)

Answer 26

Part c just wants you to find every point where the gradient is zero. So, wherever f'(x) is equal to zero.

Answer 27

Which...it looks like you already did. x=0, 7/4, -2

Answer 28

ok thank you can u help mewith another please ^^