Let $f(x)={\displaystyle \underset{x^2}{\overset{3}{}}}{e}^{1-2z}dz.$

a$)$ Find the exact $y-$intercept of the function $f(x).$

b$)$ Use Part $1$ of the Fundamental Theorem of Calculus to find $f^{\text{'}}(x).$

Make sure you use Part $1,$ not Part $2.$

c$)$ Find any inflection points of the function $f(x).$ Be sure to show your work for finding $f^{\text{'}\text{'}}(x),$ finding any critical values, testing the critical values, and finally writing any inflection points as ordered pairs $(x,f(x)).$

Please do this only using skills up to Calculus $1.$ I have so many assignments to do so I cant do this one right now. Please help me out and please make sure its correct, if I get a bad grade on this it'll bring my grade down to a C$.$ Please do it correctly, thank you $.$