If the line tangent to the graph of the function f at the point (1, 7) also passes through the point(-2, -2), then what is the value of f'(1)?

Solution:

The question gives you f(1) already, because the point (1,7) is given.

When x = 1, y = f(x) = f(1) = 7

We can find f’(1) by finding the gradient at the point f(1), which we can do because we know the tangent touches both (1, 7) and (-2, -2)

The slope or tangent of a line passing through two points can be found by using the formula,

\(m=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}\)

Now, m = \(m=\frac{7-(-2)}{1-(-2)}\)

m = \(m=\frac{9}{3}\)

m = 3

So, f’(1) = 3

Therefore, the value of f’(1) is 3.

If the line tangent to the graph of the function f at the point (1, 7) also passes through the point(-2, -2), then what is the value of f'(1)?

Summary:

If the line tangent to the graph of the function f at the point (1, 7) also passes through the point(-2, -2), then the value of f'(1) is 3.