Step 1 :Find the value of f(c) by substituting c=1 into f(x)=x^2: f(c)=f(1)=1^2=1
Step 2 :Find the derivative of f(x)=x^2: f'(x)=2x
Step 3 :Find the value of f'(c) by substituting c=1 into f'(x)=2x: f'(c)=f'(1)=2(1)=2
Step 4 :Substitute the values of f(c) and f'(c) into the linear approximation formula: L(x)=1+2(x-1)
Step 5 :Simplify the expression: L(x)=2x-1
Step 6 :Therefore, the linear approximation of f(x)=x^2 at the point (1,1) is y=2x-1