Home > Calculus > Tangent Line to a Curve

What is the equation of the line tangent to #f(x)=-x^2 + 4x - 9 # at #x=-1#?

Answer 1

Emma Aldridge

#y+14 = 6(x+1) # is the equation of tangent line in the point-slope form. The step by step explanation is given below

To find equation of tangent we need to find two things 1) Find the slope #m# 2) A point #(x_1,y_1)#

We are asked to find at #x=-1# #f(x)=-x^2+4x-9#

#f(-1)=-(-1)^2+4(-1)-9# #f(-1)=-1-4-9# #f(-1)=-14#

The point #(x_1,y_1) = (-1,-14)#

To find slope we need to find the derivative of #f(x)# at #x=-1#

#f(x) = -x^2+4x-9# #f'(x) = -2x + 4# #m=f'(-1) = -2(-1)+4# #m=2+4# #m=6#

Equation of a line passing through #(x_1,y_1)# with slope #m# is given by

#y-y_1 = m(x-x_1)#

#y-(-14) = 6(x+1)# #y+14 = 6(x+1) # is the equation of tangent line in the point slope form.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isabella Ackerman

The equation of the line tangent to f(x)=-x^2 + 4x - 9 at x=-1 is y = -3x - 6.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.