Let f(x) = 10x²(x- 7) + 4.Find the critical points c that correspond to local minima.(Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if thereare no critical points.)C =Find the critical points c that correspond to local maxima.(Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if thereare no critical points.)C =Find values at which the points of inflection occur.(Use symbolic notation and fractions where needed. Give your answer as a comma separated list. Enter DNE if there are nopoints of inflection.)X =Determine the interval on which f is concave up.Question Source: Rogawski 4e Calculus Early Transcendentals (Use symbolic notation and fractions where needed. Give your answer as a comma separated list. Enter DNE if there are nopoints of inflection.)Determine the interval on which f is concave up.(Use symbolic notation and fractions where needed. Give your answer as interval in the form (*,*). Use the symbol co forinfinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "J" depending on whether the interval isopen or closed. Enter Ø if the interval is empty.)x EDetermine the interval on which f is concave down.(Use symbolic notation and fractions where needed. Give your answer as interval in the form (*, *). Use the symbol co forinfinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval isopen or closed. Enter Ø if the interval is empty.)

Question

Let f(x) = 10x²(x- 7) + 4.Find the critical points c that correspond to local minima.(Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if thereare no critical points.)C =Find the critical points c that correspond to local maxima.(Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if thereare no critical points.)C =Find values at which the points of inflection occur.(Use symbolic notation and fractions where needed. Give your answer as a comma separated list. Enter DNE if there are nopoints of inflection.)X =Determine the interval on which f is concave up.Question Source: Rogawski 4e Calculus Early Transcendentals (Use symbolic notation and fractions where needed. Give your answer as a comma separated list. Enter DNE if there are nopoints of inflection.)Determine the interval on which f is concave up.(Use symbolic notation and fractions where needed. Give your answer as interval in the form (*,*). Use the symbol co forinfinity, U for combining intervals, and an appropriate type of parenthesis &#34;(&#34;, &#34;)&#34;, &#34;[&#34;, &#34;J&#34; depending on whether the interval isopen or closed. Enter Ø if the interval is empty.)x EDetermine the interval on which f is concave down.(Use symbolic notation and fractions where needed. Give your answer as interval in the form (*, *). Use the symbol co forinfinity, U for combining intervals, and an appropriate type of parenthesis &#34;(&#34;, &#34;)&#34;, &#34;[&#34;, &#34;]&#34; depending on whether the interval isopen or closed. Enter Ø if the interval is empty.)

Accepted Answer

Given function is f(x)=10x2(x-7)+4