Could someone help me with this question please,

2. Suppose that f is a function with f(25)=61 and f'(25)=3. If you have no further information, what is your best estimate of f(26.5)?

Question

Could someone help me with this question please,

2. Suppose that f is a function with f(25)=61 and f'(25)=3. If you have no further information, what is your best estimate of f(26.5)?

blacksteel · Answer

The derivative of a function is the slope of the function at that point. Thus, if f'(25) = 3, then we can estimate that increasing the input value of the function from 25 to 26.5, a change of  1.5, will increase the output of the function by 1.5*3 = 4.5.

Thus, given no other information, the best estimate we can give for the value of this function is f(26.5) = 61 + 4.5 = 65.5

anonymous · Answer

Ohh  okay thanks a lot for your help, I appreciate it.