solving an equation
If f(x)=x^3-8x+10, show that there are values c for which f(c) equals;
a)pi
b)-square root of 3
c)5,000,000

Question

solving an equation 
If f(x)=x^3-8x+10, show that there are values c for which f(c) equals;
a)pi
b)-square root of 3
c)5,000,000

anonymous · Answer

a. 15.87

harsimran_hs4 · Answer

for each part proceed this way...
a) pi
let there be a number c such that f(c) = pi i.e x^3 - 8x + 10 = pi
x^3 -8x +10-pi = 0
all you need to show is that there is at least one real root of this equation and you are done

anonymous · Answer

so for b is -9.05

harsimran_hs4 · Answer

what -9.05 ??

anonymous · Answer

oh I plugged something wrong. Is it, 18.66

harsimran_hs4 · Answer

10 + sqrt(3) = 11.732
x^3 -8x +11.732 = 0 for 2nd part

klimenkov · Answer

$f(x)$ is continuous, so it can possess any value between $f(a)$ and $f(b)$. If you put $a=-\infty$ and $b=\infty$, you will have, that your polynomial can possess any value from $\mathbb R$. This is the proof.

anonymous · Answer

Basically, you want to use the intermediate value theorem.