Review packet questions
- 2. Find all points on the graph of the function f(x)= Where the slope of the tangent is 2.
- 3. How to Solve For this problem because it is asking for the slope of a tangent line at a specific point, you first must take the derivative of the given equation. Because this is simple equation you can take the derivative by simply using the power rule. Once the derivative has been taken, set it equal to 2 (the given slope) because you are finding the values at which the slope is 2. After this plug your x values back into the original equation to find the y coordinates for the points.
- 4. Find all points on the graph of f (x)= At which there is a horizontal tangent line
- 5. How to Solve For this problem, first take the derivative using power rules. Now we know that horizontal lines have a slope of zero and that you are looking for all points on the graph that have a horizontal tangent line. Therefore, once you have taken the derivative you set it equal to zero and solve for x in order to find the values of x at which you have a slope of 0. After this plug your x values back into the original equation to find the y coordinates for the points .
- 6. Find f’ (x) for f (x)=
- 7. How to Solve For this problem because you have to quantities being multiplied together you would need to use the product rule to find the derivative. The formula for the product rule is f’ (x)= FS’+F’S or in other words the first quantity times the derivative of the second quantity plus the derivative of the first quantity times the second quantity.
- 8. Find f’ (x) for f (x)=
- 9. How To Solve For this problem in order to take the derivative you must use the chain rule because it is a quantity being raised to a power. For the chain rule you work outside to inside.
- 10. Find y’ if
- 11. How To Solve This problem requires the use of the implicit derivative. For the implicit derivative you follow all the usual rules for derivatives and take the derivative of everything with respect to x. Then you isolate and solve for dy/dx.
- 12. Functions f and g and their derivatives have the following values when x=5 F (5)=7, f’(5)= .5, g(5)= -9, g’(5)= -1/3. Find
- 13. How to Solve For this problem you follow the formula for the quotient rule but instead of plugging in the equations as you normally would you plug in the values. Remember to still follow lowdhigh – highdlow all over lowlow
- 14. Find y’ if
- 15. How To Solve This problem requires the use of the implicit derivative. For the implicit derivative you follow all the usual rules for derivatives and take the derivative of everything with respect to x. Then you isolate and solve for dy/dx.