ANSWER
𝑑𝑦
𝑆𝑙𝑜𝑝𝑒 = 𝑑𝑥
𝑑
𝑑𝑥
(3𝑥 3 + 4𝑥 2 − 7𝑥 + 9)
𝐴𝑝𝑝𝑙𝑦 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑟𝑢𝑙𝑒: (𝑓 ± 𝑔)′ = 𝑓′ ± 𝑔′
𝑑 𝑑 𝑑 𝑑
(3𝑥 3 ) + (4𝑥 2 ) − (7𝑥) + (9)
𝑑𝑥 𝑑𝑥 𝑑𝑥 𝑑𝑥
𝑑
(3𝑥 2 ) = 9𝑥 2
𝑑𝑥
𝑑
(4𝑥 2 ) = 8𝑥
𝑑𝑥
𝑑
(7𝑥) =7
𝑑𝑥
𝑑
(9) =0
𝑑𝑥
9𝑥 2 + 8𝑥 − 7 + 0
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦
9𝑥 2 + 8𝑥 − 7
𝐹𝑜𝑟 9𝑥 2 + 8𝑥 − 7 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑒 𝑥 𝑤𝑖𝑡ℎ 9
= 9 × 92 + 8 × 9 − 7
= 9 × 92 + 8 × 9 − 7 = 794
= 794
∴ 𝑂𝑃𝑇𝐼𝑂𝑁 𝐴
𝑑𝑦
𝑆𝑙𝑜𝑝𝑒 = 𝑑𝑥
𝑑
𝑑𝑥
(3𝑥 3 + 4𝑥 2 − 7𝑥 + 9)
𝐴𝑝𝑝𝑙𝑦 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑟𝑢𝑙𝑒: (𝑓 ± 𝑔)′ = 𝑓′ ± 𝑔′
𝑑 𝑑 𝑑 𝑑
(3𝑥 3 ) + (4𝑥 2 ) − (7𝑥) + (9)
𝑑𝑥 𝑑𝑥 𝑑𝑥 𝑑𝑥
𝑑
(3𝑥 2 ) = 9𝑥 2
𝑑𝑥
𝑑
(4𝑥 2 ) = 8𝑥
𝑑𝑥
𝑑
(7𝑥) =7
𝑑𝑥
𝑑
(9) =0
𝑑𝑥
9𝑥 2 + 8𝑥 − 7 + 0
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦
9𝑥 2 + 8𝑥 − 7
𝐹𝑜𝑟 9𝑥 2 + 8𝑥 − 7 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑒 𝑥 𝑤𝑖𝑡ℎ 9
= 9 × 92 + 8 × 9 − 7
= 9 × 92 + 8 × 9 − 7 = 794
= 794
∴ 𝑂𝑃𝑇𝐼𝑂𝑁 𝐴
