Find an equation of the tangent line to the curve y=e^x when x=−4.98.

Question

 Find an equation of the tangent line to the curve y=e^x when x=−4.98.

I don't know how to solve it 

can anybody help me, please

thank you so much.

 

Answer 1

Find an equation of the tangent line to the curve y=e^x when x=−4.98.
 Find an equation of the tangent line to the curve y=e^x when x=−4.98.
I don't know how to solve it 
can anybody help me, please
thank you so much.

 

Solution:

 

To find the equation of the tangent line to the curve, you need the slope

and a y intercept. The equation of the curve and the x coordinate point are given:

 

y=e^x when x=−4.98.

 

Answer 2

The first derivative is y' = e^x

 

The slope of the tangent line M = e^-4.98

 

Let k = M = e^-4.98

 

At x = -4.98, y = e^-4.98 so the ordered pair is (-4.98, e^-4.98)

 

the intercept is B =        y     -       M           x

                         = e^-4.98 - ( e^-4.98 )(-4.98) 

 

                          = e^-4.98 + 4.98*e^-4.98

 

                         = 5.98*e^-4.98

 

So the equation of the tangent line is

  

  y = e^-4.98 X + 5.98*e^-4.98

 

    = k X + 5.98*e^-k