Find the slope and an equation of the tangent line to the graph of the function f at the specified point.

Question

f(x)= -5/2 x²+8x+8; (-1, -5/2)

slope=?

(equation) y=?

Answer 1

y'= -5x + 8

y'(-1) = 5+8 = 13 = slope of the tangent line at the given point

tangent line is

y=13x + b plug in the point to find b

-5/2 = 13(-1) + b

b = -5/2 +13 = 21/2

y =13x + 21/2 is the tangent line

Answer 2

f(x)= -5/2 x²+8x+8

find slope at x=-1

f'(x)= -5x+8

m=-5(-1)+8=13

slope=13

equation of the tangent line

y-(-5/2)=13(x-(-1))

y+5/2=13x+13

y=13x+10.5