Question 1 - Derivatives, Tangents, and Linear Approximation Practice

Question 1

00:00Est. 2 min

Marks:+2.000.00

Passage

A satellite dish is shaped like a parabola, and its height above the ground (in meters) at a horizontal position

x

metres is given by:

f(x) = ax^2 - 12x + 10, \quad a \in \mathbb{R} \setminus \{0\}

An engineer places a ladder that follows the path of a line given by

y = 8x + 3

. At the point where

x = 1

, the slope of the satellite dish's curve is the same as the slope of the ladder. Use this information to answer the given subquestions.

Question

Find the value of

a

Comprehension

Medium Difficulty

13 July 2025

Your answer