Home > Calculus > Tangent Line to a Curve

What is the equation of the line tangent to #f(x)=(x+7)^2# at #x=2#?

Answer 1

Aurora Alvarado

#y=2x+45#

#f(x)=(x+7)^2#

Using the chain rule:

#f'(x)=2(x+7)^1xx(d(x+7))/(dx)#

#:.f'(x)=2(x+7)#

The tangent line is of the form:

#y=mx+c#

#:.m=2(x+7)#

When #x=2rArr#

#m=2(2+7)=18#

#f(2)=(2+7)^2=81#

#:.81=(18xx2)+c#

#:.c=81-36=45#

So the tangent line becomes:

#y=2x+45#

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

Answer 2

Elijah Abram

The equation of the line tangent to f(x)=(x+7)^2 at x=2 is y = 4x + 9.

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.

Trending questions

Not the question you need?

HIX Tutor

Solve ANY homework problem with a smart AI

98% accuracy study help
Covers math, physics, chemistry, biology, and more
Step-by-step, in-depth guides
Readily available 24/7