**Problem : ***f* (*x*) = 2*x*. Find *f'*(*x*)

f'(x) | = | ||

= | |||

= | |||

= 2 | |||

= 2 |

**Problem : ***f* (*x*) = - *x*^{2}. What is the *f'*(*x*)?

f'(x) | = | ||

= | |||

= | |||

= - (2x + h) | |||

= - 2x |

**Problem : **
Find the slope of the line perpendicular to the tangent of the graph of *f* (*x*) = - *x*^{2}
at *x* = 1.

This is the slope of the tangent. The perpendicular to the tangent has a slope that is the negative reciprocal of this, which is .

**Problem : **
Find *f'*(1) for *f* (*x*) = - *x*^{2} without solving for *f'*(*x*) first.

If we are trying to find the derivative at a single point only, we can substitute that point directly into the limit of the difference quotient

f'(1) | = | ||

= | |||

= | |||

= | |||

= - (2 + h) | |||

= - 2 |

**Problem : **
Give an example of a function that is not differentiable at *x* = *a*.

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