For this question, it would be easier if you have some prior knowledge in integration and anti-derivatives, but I'll try to explain it without using those concepts.
So, when you differentiate a constant, you get zero, right? As f'(x) = g'(x), you can use this concept to find a general formula for f(x), which would be tan-1(x) + some constant. When you differentiate f(x), this "some constant" would become zero, making f'(x) = g'(x).
Hi,
Thank you for your question.
For this question, it would be easier if you have some prior knowledge in integration and anti-derivatives, but I'll try to explain it without using those concepts.
So, when you differentiate a constant, you get zero, right? As f'(x) = g'(x), you can use this concept to find a general formula for f(x), which would be tan-1(x) + some constant. When you differentiate f(x), this "some constant" would become zero, making f'(x) = g'(x).
Now, we just have to find this "some constant".
f(1) = tan-1(1) + some constant = 8
pi/4 + some constant = 8
some constant = 8 - pi/4.
Hence, f(x) would equal tan-1(x) + 8 - pi/4
Does this answer your question?