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Question

# Consider the following statements S1: If x3+y2=5(xy−1), then dydx at (1,3) is equal to 12 S2: If xe=ey, then dydx at x=1 is equal to e S3: If f(x) is a linear polynomial, then f′(sinx)+f′′(sinx) is constant. Which of the following is/are correct about the truth value of above statements

A
S1 is false and S3 is true
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B
S2 and S3 both are true
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C
S1 and S3 both are true
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D
S1 is true and S2 is false
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Solution

## The correct option is C S1 and S3 both are trueS1:3x2+2yy′=5(y+xy′) at (1,3); 3+6y′=5(3+y′) ⇒y′=12 S2:xe=ey elnx=y ⇒y′=ex at x=1,y′=e S3:f(x)=ax+b⇒f(sinx)=asinx+b f′(sinx)⋅cosx=acosx⇒f′(sinx)=a f′′(sinx)=0 ⇒f′′(sinx)+f′(sinx)=a (constant)

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