Home > Calculus > Tangent Line to a Curve

How do you find the equation of a line tangent to the function #y=4x-x^2# at (2,4)?

Answer 1

Evelyn Agard

#y=4#

#"the slope of the tangent is "dy/dx" at x =2"#

#dy/dx=4-2x#

#x=2tody/dx=4-4=0#

#"thus tangent is parallel to the x-axis"#

#"with equation "y=4# graph{(y-4x+x^2)(y-0.001x-4)=0 [-10, 10, -5, 5]}

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

Answer 2

Ezekiel Alexander

To find the equation of a line tangent to the function y=4x-x^2 at (2,4), we need to find the slope of the tangent line at that point.

To find the slope, we take the derivative of the function y=4x-x^2 with respect to x.

The derivative of y=4x-x^2 is dy/dx = 4 - 2x.

Substituting x=2 into the derivative, we get dy/dx = 4 - 2(2) = 4 - 4 = 0.

Since the slope of the tangent line is 0, the equation of the tangent line is y = 4.

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.