List of top Mathematics Questions on Applications of Derivatives asked in CBSE CLASS XII

In an agricultural institute, scientists conduct experiments with varieties of seeds to grow them in different environments for producing healthy plants and obtaining higher yields.
A scientist observed that a particular seed grew very fast after germination. He recorded the growth of the plant from the time of germination and modeled its growth with the function:
Given:
\( f(x) = \frac{1}{3}x^3 - 4x^2 + 15x + 2 \),   \( 0 \leq x \leq 10 \)
where \( x \) is the number of days the plant is exposed to sunlight.
On the basis of the above information, answer the following questions: 

If f (x) = 3x²+15x+5, then the approximate value of f (3.02) is

It is given that at x = 1, the function x⁴−62x²+ax+9 attains its maximum value, on the interval [0, 2]. Find the value of a.

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41−24x−18x²

At what points in the interval [0, 2\(\pi\)], does the function sin 2x attain its maximum value?

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i). f(x) = x² (ii). g(x) = x³ − 3x (iii). h(x) = sinx + cos, 0 <x<\(\frac{\pi}{2}\) (iv). f(x) = sinx − cos x, 0 < x < 2π (v). f(x) = x³ − 6x² + 9x + 15(vi) g(x)=\(\frac{x}{2}\)+\(\frac{2}{x}\)>0 (vii).g(x)=\(\frac{1}{x^2}\)+2(viii). f(x)=x√1-x,x>0