## ChrisV 3 years ago Find the derivative of f(x)=5-|x-5|

1. lgbasallote

this is d/dx (5) - d/dx (x-5) derivative of 5 = 0..and the derivative of x-5 = 1 so.. 0-1 = -1

2. ChrisV

wouldnt you have a +/- value since its absolute value?

3. CoCoTsoi

As there is a absolute value, we have to consider two cases. f(x)=5-|x-5| case i), for x>5 f(x) = 5-(x-5) = 5-x+5 =10-x f'(x) =-1 case ii) for x<=5, f(x)= 5-(-(x-5) ) =5+(x-5) =x f'(x)=1

4. lgbasallote

oh wait..that was absolute value?? so sorry! thought they were parentheses

5. lgbasallote

6. Rohangrr

If the problem is 1/(x - 5), then, by the power rule, the derivative is: -1/(x - 5)^2 The slope, m, of the tangent line is the derivative evaluated at the x-coordinate of the point. Plug in -4 for x: m = -1/(-4 - 5)^2 = -1/81 Then solving y = mx + b for the y-intercept after plugging in the point: -1/9 = 4/81 + b b = -1/9 - 4/81 = -13/81 Tangent line equation is: y = -1/81*x - 13/81 Hope this helps.

7. brinethery

1/(x-5) = (x-5)^-1. Then you use the chain rule to take the derivative.

8. dpaInc

|dw:1333266207662:dw| you can treat it as a piece-wise function. so if you want the derivative, f'(x) will be something different depending on the x you look at...