f(x)= x + sqrt(x)
1. The point (9, 12) belongs to the function
f(9) = 9 + sqrt(9) = 9+3 = 12. Ok.
2. The slope m of the tangent line is f’(9):
f’(x) = 1 + 1/(2sqrt(x))
m= f’(9) = 1 + 1/(2sqrt(9)) = 1 +1/6 = 7/6
3. The equation of tangent line is
y – 12 = 7/6 (x -9)
6y – 72 = 7x – 63
7x – 6y = -9
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Verified answer
f(x)= x + sqrt(x)
1. The point (9, 12) belongs to the function
f(9) = 9 + sqrt(9) = 9+3 = 12. Ok.
2. The slope m of the tangent line is f’(9):
f’(x) = 1 + 1/(2sqrt(x))
m= f’(9) = 1 + 1/(2sqrt(9)) = 1 +1/6 = 7/6
3. The equation of tangent line is
y – 12 = 7/6 (x -9)
6y – 72 = 7x – 63
7x – 6y = -9