$[5$ pts$]$ Consider the function $h(x)=\frac{1}{3}{x}^3\frac{5}{2}{x}^2-14x.$

a$)$ Find $h^{\text{'}}(x).$

b$)$ Determine all critical numbers for $h(x).$

c$)$ Determine whether each critical number is the location of a local maximum, a local minimum, or neither. Be sure to use calculus to justify your answers.d$)$ Find $h^{\text{'}\text{'}}(x).$

e$)$ Determine the intervals of concavity for $h(x)?$ That is$,$ where is $h$ concave up and where is $h$ concave down?