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

There are none.

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.