# Thread: Applications of Differentiation involving e to power of x

1. ## Applications of Differentiation involving e to power of x

Find the equation of the tangent to the curve y = e to the power x at the point where x = a. Hence find the equation to the tangent to the curve y = e to the power x which passes through the origin. The straight line y = mx intersects the curve y = e to the power x in two distinct points. Write down an inequality for m.

2. Hi

The equation of the tangent of the curve representing f at abscissa a is
$\displaystyle y = f'(a)(x-a)+f(a)$

When $\displaystyle f(x) = e^x$ you get $\displaystyle y = e^a x + e^a(1-a)$

It passes through the origin when $\displaystyle e^a(1-a) = 0$ which gives a = 1

3. Originally Posted by puggie
Find the equation of the tangent to the curve y = e to the power x at the point where x = a. Hence find the equation to the tangent to the curve y = e to the power x which passes through the origin. The straight line y = mx intersects the curve y = e to the power x in two distinct points. Write down an inequality for m.

the curve $\displaystyle y=e^x$ dose not pass through the origin how you can find the tangent line of it at (0,0)

$\displaystyle e^x=0$ you can't find a value of x which make that equation true

the tangent for $\displaystyle y=e^x$ at x=a first find
y when x=a you will have

$\displaystyle y=e^a$

now derive y $\displaystyle y'=e^x$ sub a in it you will get the slope which equal $\displaystyle e^a$ finally the tangent line of y is

$\displaystyle y-e^a=e^a(x-a)$

then
$\displaystyle y=e^x$ can't intersect $\displaystyle y=mx$ in tow points y=mx pass through the origin but $\displaystyle y=e^x$ dose not pass through it

it is clear or not ........