3.1 Derivatives of Polynomials and Exponentials

Question 1

how to find the points on a curve with the tangent is horizontal?

Answer 1

1. find the derivative of the function given
2. set the first derivative equation to zero and solve for all x’s
3. find the points of all x

Question 2

how to find the acceleration at a certain time given a position function? what are the units?

Answer 2

1. find the second derivative
2. plug the t values given in the second derivative to find acceleration at that time
3. the units are cm/s^2

Question 3

what is the derivative of e to the power of x

Answer 3

it is just itself

Question 4

how to find the point on a curve of a function given where the tangent line is parrallel to another function given.

Answer 4

1. find the derivative of the first function given
   2.find the slope of the second function
2. set the first derivative equal to the slope of the second function and isolate for x
3. create a point for the x value found