Thread: Simple as it sounds?

1. Simple as it sounds?

Cousin had this question:

Determine the point (a,f(a)) for which f'(a)=a given that f(x)=-x^2+3x-7

We both did this question the same way, got the same solution, but textbook disagrees.

Can anyone try so we know we're not going crazy?

Thanks

2. Re: Simple as it sounds?

Originally Posted by boyohboy
Cousin had this question:

Determine the point (a,f(a)) for which f'(a)=a given that f(x)=-x^2+3x-7

We both did this question the same way, got the same solution, but textbook disagrees.

Can anyone try so we know we're not going crazy?

Thanks
We can't catch a possible mistake unless we know what you did. So... How did you solve this?

-Dan

3. Re: Simple as it sounds?

$f(x) = -x^2 + 3x -7$

$f'(x) = -2x + 3$

solve

$a = -2a+3$

$3a = 3$

$a=1$

are you going crazy?

4. Re: Simple as it sounds?

Originally Posted by boyohboy
Determine the point (a,f(a)) for which f'(a)=a given that f(x)=-x^2+3x-7
We both did this question the same way, got the same solution, but textbook disagrees.
\begin{align*}f(x)&=-x^2+3x-7 \\f^{\prime}(x)&=-2x+3\\\\a&=-2a+3\\3a&=3\\a&=1 \end{align*}