Find an equation of the tangent line to the curve at the given point. y = 4x^2 - x^3, (1, 3)

Question

Please help me 

Answer 1

y = 4x² - x³

 

 

The derivative is the slope of the tangent line.  We find the derivative of the given function.

 

y' = 8x - 3x²

 

 

Evaluate y' by plugging in x=1.

 

y' = 5

 

 

The equation of the tangent line so far is    y = 5x + b

 

 

Next, plug in the values of the coordinate (1, 3) to find b.

 

3 = 5(1) + b

 

3 = 5 + b

 

-2 = b

 

 

The equation of the tangent line is

 

y = 5x - 2