JEE Main 2022 · 30 Jun · Shift 1 · Mathematics Q22

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MathematicsInteger+4 / -1Question 22 of 90

Let for $f(x)=a_0x^2+a_1x+a_2$ , $f'(0)=1$ and $f'(1)=0$ . If $a_0,a_1,a_2$ are in an arithmatico-geometric progression, whose corresponding A.P. has common difference 1 and corresponding G.P. has common ratio 2, then $f(4)$ is equal to ______.

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Answer and worked solution

Official answer: 2

AGP. $a_0=ab$ , $a_1=2b(a+1)$ , $a_2=4b(a+2)$ . $f'(0)=a_1=1$ , $f'(1)=2a_0+a_1=0$ : $ab=-\frac12$ , $b=1$ , $a=-\frac12$ .

f(x) $=-\frac12x^2+x+6$ ; $f(4)=2$ .

Answer: 2

Topics:Arithmetico-geometric series Derivatives of standard functions

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JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 22