Given:
The function is:
[tex]h(t)=-4.9t^2+24t+10[/tex]Find-:
The maximum height of function.
Explanation-:
The critical points:
[tex]h(t)=-4.9t^2+24t+10[/tex]The function derivative is;
[tex]\begin{gathered} h(t)=-4.9t^2+24t+10 \\ \\ h^{\prime}(t)=-4.9\times2t+24 \\ \\ h^{\prime}(t)=-9.8t+24 \end{gathered}[/tex]The critical value of function is h'(t) = 0
[tex]\begin{gathered} h^{\prime}(t)=-9.8t+24 \\ \\ h^{\prime}(t)=0 \\ \\ -9.8t+24=0 \\ \\ 9.8t=24 \\ \\ t=\frac{24}{9.8} \\ \\ t=2.45 \end{gathered}[/tex]The maximum value is:
[tex]\begin{gathered} h(t)=-4.9t^2+24t+10 \\ \\ h(2.45)=-4.9(2.45)^2+24(2.45)+10 \\ \\ h(2.45)=39.3878 \end{gathered}[/tex]The maximum value is 39.3878
