For what value of the number k is the following function differentiable at x=2 f(x) = {2x + 1 if x<2
k x=2
3x-1 x>2}

For f(x) to be differentiable at 2, k = 5.

Step-by-step explanation:

For f(x) to be differentiable at x = 2, f(x) has to be continuous at 2.

For f(x) to be continuous at 2, the limit of f(2 – h) = f(2) = f(2 + h) as h tends to 0.

Now,

f(2 – h) = 2(2 – h) + 1 = 4 – 2h + 1 = 5 – 2h.

As h tends to 0, lim (5 – 2h) = 5

Also

f(2 + h) = 3(2 + h) – 1 = 6 + 3h – 1 = 5 + 3h

As h tends to 0, lim (5 + 3h) = 5.

So, for f(2) to be continuous k = 5

what is the question? i am guessing you are looking for the area.

to find an area, you have to do length x width.

in this case, it would be 12 ft x 4 ft = 48 sq. ft