Posted by **Rachael** on Sunday, June 9, 2013 at 1:12am.

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

FŒ(5)=

The equation of the tangent line is y = x + .

Check your answer for yourself by graphing the curve and the tangent line.

- Calculus -
**Reiny**, Sunday, June 9, 2013 at 8:49am
f(5) = 125 - 35 + 5 = 95

f(5+h) = (5+h)^3 - 7(5+h) + 5

= h^3 + 15h^2 +68h + 95 --- (I'll let you check that

derivative = Lim ( f(h+5) - f(5) )/h as h ---> 0

= lim ( h^3 + 15 h^2 + 68h = 95 - 95)/h

= lim h^2 + 15h + 68 , as h --> 0

= 68

so equation of tangent at (5,95)

y - 95 = 68(x-5)

y = 68x - 340 + 95

y = 68x - 245

## Answer This Question

## Related Questions

- Calculus - Find the equation of the tangent line to the curve (piriform) y^2=x^3...
- Math - The point P(8, −3) lies on the curve y = 3/(7 − x). (a) If Q ...
- Calculus AB - Could someone please help me with these tangent line problems? 1) ...
- calculus - Write the equation of the tangent line to the curve at the indicated ...
- calculus - To find the equation of a line, we need the slope of the line and a ...
- Calculus AB - Sorry but I've got a lot of problems that I don't understand. 1) ...
- calculus - f(t) = − 4 t2 − t− 6 Find the equation of the line...
- calculus - 1. Which of the following expressions is the definition of the ...
- Calculus - Use implicit differentiation to find an equation of the tangent line ...
- Calculus - Use implicit differentiation to find an equation of the tangent line ...

More Related Questions