# Calculus

posted by .

I am not sure what to do here:

Find the derivative (f '(x) using the limit process

a). f(x)= 2x^2+5x+2 find f ' (2)

b.) Find the equation of the Tangent Line at (1,5)

• Calculus -

suppressing the limit notation for the moment,

f' = [f(x+h)-f(x)]/h
f' = [(2(x+h)^2 + 5(x+h) + 2) - (2x^2 + 5x + 2)]/h
f' = [(2x^2 + 4xh + 2h^2) + (5x + 5h) + 2 - (2x^2 + 5x + 2)]/h
f' = (4xh + 2h^2 + 5h)/h
f' = 4x + 5 + 2h
lim as h->0 = 4x+5
-------------------------
f'(1) = 9

(y-5) = 9(x-1)

• Calculus -

Thank you so so much! I finally understand what to do! :)

## Similar Questions

1. ### Calculus - Damon

Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point. So I found the derivative which is 3x^2. Let (a, a3) be the point of tangency. 3x^2 = (a3 - 1/4)/(a-0) I'm not sure how to solve …
2. ### calculus

Consider the function. 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
3. ### Derivative Calculus

I just need my answers checked. 1) Find the derivative. f(x)=3x^5/4 - 8/9x^9/8 + x^2 - 9x + 1 Answer: f’(x)= 15/4x^1/4 - x ^1/8 + 2x -9 2) Let f(x)= 7x^3 - 9x. Find f’(5) Answer: f’(x)=21x^2-9 f’(5)=516 3) Find the given limit …
4. ### Calculus

If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x …
5. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
6. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
7. ### Calculus

1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^-1 x is 1/(|x|*sqrt(x^2 -1)). …
8. ### Calculus

Using the definition of the derivative, find the equation of the tangent line to y=2x-1/2 at (1/2,-1) Thanks!!
9. ### Calculus

Find an equation of the tangent line to the graph of f at the given point. f(x) = x + (4/x), (4,5) I tried using the limit process a lot, but it didn't quite work. If possible, please use the limit process. Thanks a lot to whoever …
10. ### Math (equation of tangent line)

Consider the implicit equation 2xy-1=(x+y+1)^2 a) Compute and solve for the derivative dy/dx as a function of x and y. b) Find the equation of the tangent line to the graph of the above when y=-1. For part a, I found the derivative …

More Similar Questions