Question

Is a tangent line able to have a exponential slope? This seems contradictory but this is what is used in the rate of change video.

Answer 1

No the tangent line as it's name indicate is a line and cannot have an exponential slope. by the way the slope is a number. So saying exponential slope doesn't have a clear meaning (exponential number ? function yes!, number no!)

Maybe your confusion comme form the fact that the function used to find the tangent slope can be an exponential function. Remember that the tangent slope at point \(a \) of a funtion \(f(x) \) can be \(f^'(a) \) if \(f\) has a derivative in \(a\).

Example:
\(f(x)=e^{2x^5+3}, \ f^'(x)=2x^4.e^{2x^5+3}\). \(f^'(x)\) here is an exponential function. So the slopes of the tangents for \(f\) will evolve exponentialy with \(a\)

Answer 2

Thanks! well explained

Answer 3

Good explanation