1. ## Need help checking answer!!

Left f(x) be a continuous function f(2)=10, f’(2)=-4 and f’’(x)=-6 for all X. Find the value of f(2.5)
since the slope is the derivative (-4), I plugged that in to y=mx+b and got 10=-4(2)+b, to solve for b and got 18=b. So my equation is y=-4x+18. I then solved for y, which is 8. So f(2.5)=8.....is that right?

2. ## Re: Need help checking answer!!

first off $f^{\prime \prime}(x) = -6,~\forall x$

thus

$f^\prime(x) = -6x+c_1$

$f(x) = -3x^2 + c_1 x + c_0$

$f^\prime(2) = -4 \Rightarrow c_1 = 8$

so $f(x) = -3x^2 + 8x + c_0$

$f(2) = 10 \Rightarrow c_0 = 6$

$f(x) = -3x^2 + 8x + 6$

$f(2.5) = 7.25$

3. ## Re: Need help checking answer!!

Originally Posted by tomas
Left f(x) be a continuous function f(2)=10, f’(2)=-4 and f’’(x)=-6 for all X. Find the value of f(2.5)
since the slope is the derivative (-4), I plugged that in to y=mx+b and got 10=-4(2)+b, to solve for b and got 18=b. So my equation is y=-4x+18. I then solved for y, which is 8. So f(2.5)=8.....is that right?
You are assuming that the function is linear which can't be true because a linear function has second derivative 0, not -6.