Home > Calculus > Tangent Line to a Curve

What is the equation of the tangent line of #f(x)=4x^3+12x^2+9x+7# at #x=-3#?

Answer 1

Isabella Ackerman

y = 45x + 115

to determine the tangent's equation in the formula y = mx + c.

We need to determine the value of c as well as the gradient, m.

We obtain m by evaluating f'(-3) and c by evaluating f(-3) respectively.

Differentiate using the #color(blue)" power rule " #

#f'(x) =12x^2+24x+9#

and #f'(-3)=12(-3)^2+24(-3)+9=108-72+9=45#

Now f(-3) #=4(-3)^3+12(-3)^2+9(-3)+7=-20#

Y = 45x + c is the partial equation; to find c, enter (-3,-20) into the partial equation.

Consequently, -20 = -135 + c → c = 115

Tangent equation: y = 45x + 115

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

Answer 2

Evelyn Agard

The equation of the tangent line of f(x)=4x^3+12x^2+9x+7 at x=-3 is y = -18x - 19.

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.