If F(t) = 4t + 7, find F(3 + H) - F(3)/ H

I dont know how to input this, i have the answers in the back but that doesnt help me understand.

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This problem relates to taking the derivative in calculus, for which one formula is to take the limit as h-->0 for the formula

[ f(a+h)-f(a) ]/ h

In this case you make the substitutions 3+H and 3 into the F(t)=4t+7:

F(3+H)-F(3) /H =

[ 4(3+H)+7 - (4*3+7) ] / H =

(12 + 4H + 7 - 12 - 7 ) / H =

4H/H =

4.

There is no need to take the limit here as H-->0 as H divides out. I realize the problem as stated did not ask for that, but it seems likely that this is related to the derivative in calculus from the way it is structured.

If you wished to find the derivative, you would lower the power on the variable by 1 and cancel any constants, so that for F(t)=4t+7 the first derivative F'(t)=4. This is the same result.

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