I need help!

[mboudreaux23]

Simplify the quotient (f(x)-f(a))/(x-a), and then guess the slope of the line tangent to the graph of f at (a,f(a)).
f(x)=x^2; a=3

I've only been able to set up the problem and then from there, I'm lost.

 

[Deleted member 4993]

Simplify the quotient (f(x)-f(a))/(x-a), and then guess the slope of the line tangent to the graph of f at (a,f(a)).
f(x)=x^2; a=3

I've only been able to set up the problem and then from there, I'm lost.

What is the expression for f(a)?

What is the expression for [f(x)-f(a)]?

What is the expression for [f(x)-f(a)]/(x-a)?

[edited]

 

[mboudreaux23]

the expression for f(a) isn't given.

the expression for [f(x)-f(a)] is [x^2-f(a)].

and the expression for [f(x)-f(a)]/(x-a) is [x^2-f(a)]/x-3.

[f(x)-f(a)]/(x-a) is the equation and f(x)=x^2; a=3 is the given information to be able to solve the equation.

 

[Deleted member 4993]

the expression for f(a) isn't given<<< f(a) = f(x) - where you have replaced 'x' by 'a'. so f(a) = a^2

the expression for [f(x)-f(a)] is [x^2-f(a)]. <<< f(x) - f(a) = x^2 - a^2

and the expression for [f(x)-f(a)]/(x-a) is <<< [x^2 - a^2]/(x-a) ..... simplify this expression by factorising the numerator and eleminating common factor.


[f(x)-f(a)]/(x-a) is the equation


and f(x)=x^2; a=3 is the given information to be able to solve the equation.

 

[mboudreaux23]

Thank you!