Wednesday

September 17, 2014

September 17, 2014

Posted by **Irene** on Monday, June 14, 2010 at 3:35pm.

f (x) = 5x3 + 3x

(a) Compute the derivative at x = 3 using the limit definition.

f '(3) =

(b) Find an equation of the tangent line.

2

- calculus -
**Reiny**, Monday, June 14, 2010 at 5:07pmevaluate f(3)

evaluate (3+h) and simplify

then take

Limit [ (f(3+h) - f(3) ]/h as h --->0

You should be able to factor out an h from the top which would then cancel the h in the bottom

you should get

f'(3) = 138

b) when x=3, y = 138 (that's a coincidence)

so you have

slope of tangent is 138 and (3,138) is a point on it

y = 138x + b , plug in the point

138 = 138(3) + b

b = -276

so y = 138x - 276 is the tangent equation

**Answer this Question**

**Related Questions**

calculus - find the limit of f'(x) = 1/(√x) using the limit definition of ...

calculus - find the limit of f'(x) = 1/(√x) using the limit definition of ...

Calculus (lim) - consider the statement lim x³-6x²+11x-6 / x-1 = 2 x->1 Using...

CALCULUS help! =) - find the derivative of f(x)=3x^2-x using the limit ...

calculus - Find the derivative of the function using the definition of ...

applied calculus - 3. a) Write out the limit definition for the derivative of y...

Calculus derivatives - f(a) = a + √a (a) Find the derivative of the ...

Calculus - Sorry for posting another quesiton..; f(x) = { -7x^2 + 7x for x<=...

CALCULUS HELP - Find the second derivative for the function 5x^3+60x^2-36x-41 ...

Calculus - Find the derivative of the function using the definition of a ...