1. Let \( f: R \rightarrow R \) be a differentiable function having non-zero derivative for all real values of \( x \). Consider the curves \( C_{1}: y=f(x) \) and \( C_{2}: y=\int_{-\infty}^{x} f(t) d t \). \( C_{1} \) passes through \( (0,1) \) and \( C_{2} \) passes through \( \left(0, \frac{1}{2}\right) \).If the tangents drawn to \( C_{1} \) and \( C_{2} \) at points having equal abscissae intersect always on \( x \)-axis then the value of \( [f(1)] \) where [.] denotes greatest integer function is equal to (7)

Question

1. Let \( f: R \rightarrow R \) be a differentiable function having non-zero derivative for all real values of \( x \). Consider the curves \( C_{1}: y=f(x) \) and \( C_{2}: y=\int_{-\infty}^{x} f(t) d t \). \( C_{1} \) passes through \( (0,1) \) and \( C_{2} \) passes through \( \left(0, \frac{1}{2}\right) \).If the tangents drawn to \( C_{1} \) and \( C_{2} \) at points having equal abscissae intersect always on \( x \)-axis then the value of \( [f(1)] \) where [.] denotes greatest integer function is equal to