consider the function g(x)=x^3+5x^2-4x+4.determine:
1)g(37)
2)the value of x between zero and a hundred such that g(x)=145456
how do i do this?
1) put in 37 for x, and compute.
2) put in 145456 in for g(x), and solve for x.
for the first one, just substitute 37 for x and evaluate
for the second one
x^3 + 5x^2 - 4x + 4 = 145456
x^3 + 5x^2 - 4x - 145452 = 0
at this point you will need a programmable calculator which solves any equation, or
use Newton's Method, or
go to an online "equation solver"
I went to
http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=equations&s2=solve&s3=basic
and it gave me an exact value of x=51
To determine the value of g(37), you simply substitute 37 for x in the function g(x) and compute the result. In this case, we have g(37) = 37^3 + 5(37)^2 - 4(37) + 4. Evaluating this expression gives you the answer.
To find the value of x between zero and a hundred such that g(x) = 145456, you need to set up an equation. In this case, we have the equation g(x) = x^3 + 5x^2 - 4x + 4 = 145456. Rearranging the equation, we get x^3 + 5x^2 - 4x - 145452 = 0.
At this point, you have a few options to solve the equation. You can use a programmable calculator with an equation-solving feature, such as a graphing calculator, to find the exact solution. Alternatively, you can use numerical methods, such as Newton's Method, to approximate the solution. Another option is to use an online "equation solver" tool, which can give you the exact value of x.
In this case, a quick online search led to a website that solves equations. By inputting the equation x^3 + 5x^2 - 4x - 145452 = 0 into this website, it provided the exact solution x = 51.