Question

Show that the curve y = 2e^x + 3x + 5x^3 has no tangent line with slope 2. . . So far, I've set it's derivative to 2... now I'm tempted to take natural logs, but it doesn't seem to lead me anywhere

Answer 1

We are given with the equation y = 2e^x + 3x + 5x^3. the tangent line of the curve is determined through differentiation the equation. Hence the first derivative is expressed as y' = 2e^x + 3 + 15x^2. when y' or slope is 2, x can't be solved. Hence there is no tangent line with slope 2.