Question

Alright, got another calc 1 question.

Show that the curve y=2e^x+3x+5x^3 has no tangent line with slope 2.

I am still a little confused on how to work with (coefficient)e^(power) when it comes to derivation and am stuck.

Answer 1

\(\dfrac{d}{dx}e^{x} = e^{x}\) -- That's it.

\(\dfrac{dy}{dx} = 2e^{x} + 3 + 15x^{2}\) -- Okay, prove that this expression NEVER takes on the value 2.