What is the instantaneous rate of change of $f(x)=x-e^(x^2-7)$ at $x=3$ ?

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Answer 1 · 2016-06-04T03:02:24

$f' (3)=1-6*e^(2)$
$f' (3)=-43.33433659$

Instantaneous rate of change is the first derivative $f' (x)$

From the given $f(x)=x-e^(x^2-7)$

The first derivative is

$f(x)=x-e^(x^2-7)$

$f' (x)=1-e^(x^2-7)*d/dx(x^2-7)$

$f' (x)=1-e^(x^2-7)*(2x-0)$

$f' (x)=1-2x*e^(x^2-7)$

at $x=3$

$f' (3)=1-2*(3)*e^(3^2-7)$

$f' (3)=1-6*e^(2)$

God bless...I hope the explanation is useful.

What is the instantaneous rate of change of f(x)=x-e^(x^2-7) f(x)=x-e^(x^2-7) at x=3 x=3 ?