Question

Find the value(s) of x where the tangent to the graph of y=e^5x is parallel to the
line 10x + y = 17

Answer 1

Answer:

There are none.

Step-by-step explanation:

No calculus involved:

The line, in slope-intercept form, has equation $y=-10x+17$, ie is always decreasing (easy to spot applying the definition)

Meanwhile, $y=e^{5x}$ is always increasing over its domain.

At no point the tangent will be decreasing.

Let's use calculus

We are to solve the equation $y'(x) = -10 \rightarrow 5e^{5x} = -10 \rightarrow e^{5x}=-2$ which has no real solutions.