Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of

Step 1: Find the derivative of the function f(x) = x(4-x)^3 using the product rule and chain rul

Find f'(x) and find the equation of the line tangent to the...

Transcript

00:01 Okay, so i am going to find f prime of x, which is the derivative of this function.

00:08 This function is a product, so i'm going to use product rule, which says i want the first function, which is x, times the derivative of the second.

00:20 Well, the second is the 4 minus x quantity cubed, and that is a chain rule.

00:26 So i'm going to drop that three down in front.

00:28 I have 4 minus x squared times negative 1 plus the second function times the derivative of the first, which is just x.

00:47 Okay, let's clean that up a little bit before we plug in our number.

00:52 So we have x times 3 times negative 1, so that's negative 3x times 4 minus x squared, plus one times anything is just itself.

01:06 I have 4 minus x cubed.

01:11 Now i can take out a 4 minus x factor.

01:16 Actually, i can take out two of them because that's common to both of these terms.

01:22 And that is going to leave me with, when i take that out, negative 3x plus, and then i just have one, four minus six.

01:33 X almost done cleaning up 4 minus x quantity squared times let's see that's negative 3x and negative x negative 4x plus 4 okay so here's my derivative now i want to write an equation of a tangent line so what do i need for an equation i need a point and i need slope all right so i have the x coordinate to my point.

02:18 I need to go and get the y coordinate by plugging two into the original function...

Question

Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = x(4 - x)^3 ; x = 2 f'(x) =

Question

Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = x(4 - x)^3 ; x = 2 f'(x) =

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