Find all points on the graph of the function f(x)=Where the slope of the tangent is 2. xxx 233 24

How to SolveFor 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.

Find all points on the graph of f (x)=

At which there is a horizontal tangent line22 34 xx

How to SolveFor 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.

Find f’ (x) for f (x)= ))(cos( 2 xx

How to SolveFor 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.

Find f’ (x) for f (x)= 43 )73( xx

How To SolveFor 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.

Find y’ if 263 xyyx

How To SolveThis 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.

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

)5(

)5(

f

f

dx

dy

How to SolveFor 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

Find y’ if 4323 xyyx

How To SolveThis 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.