James Stewart

ISBN: 9781305270343

Textbook Problem

Find an equation of the tangent line to the curve at the given point.

y = 4x – 3x², (2, –4)

To determine

To find: The equation of the tangent line to the curve at the given point.

The equation of the curve is y=4x−3x2.

The curve passing through the point (2,−4).

Formula used:

The slope of the tangent curve y=f(x) at the point P(a,f(a)) is,

m=limx→af(x)−f(a)x−a (1)

The equation of the tangent line to the curve y=f(x) at the point (a,f(a)) is,

y−f(a)=f′(a)(x−a) (2)

Calculation:

Obtain the slope of the tangent line to the curve at the point (2,−4).

Substitute a=2 and f(a)=−4 in equation (1),

m=limx→2f(x)−f(2)x−1=limx→2(4x−3x2)−(−4)x−2=limx→2−3x2+4x+4x−2=limx→2−(3x2−4x−4)x−2

The factors of (3x2−4x−4) is (3x+2) and (x−2)

Check out a sample textbook solution.

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Single Variable Calculus: Early Tr...

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Find an equation of the tangent line to the curve at the given point. y = 4x – 3x2, (2, –4)

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Find an equation of the tangent line to the curve at the given point.

y = 4x – 3x², (2, –4)